Yep, the Vivaro will pull it no problem.
My 2004 1.9 Traffic pulls my 6.5 vipermax without too much fuss. Even manages to get into 6th gear from time to time.
The engine on the 1.9 is fantastic, only 100hp but very well geared for towing.
I used to use it for launching our Valiant 570 on some pretty steep slipways over here in France, ...never had an issue.
Hope this helps